For outcomes k in 0 to K, slope vector a, intercept vector c, and latent ability vector theta,
the response probability function is
$$\mathrm P(\mathrm{pick}=0|a,c,\theta) = 1- \mathrm P(\mathrm{pick}=1|a,c_1,\theta)$$
$$\mathrm P(\mathrm{pick}=k|a,c,\theta) = \frac{1}{1+\exp(-(a\theta + c_k))} - \frac{1}{1+\exp(-(a\theta + c_{k+1}))}$$
$$\mathrm P(\mathrm{pick}=K|a,c,\theta) = \frac{1}{1+\exp(-(a\theta + c_K))}$$
whether to use a multidimensional model.
Defaults to TRUE.
Value
an item model
Details
The graded response model was designed for a item with a series of
dependent parts where a higher score implies that easier parts of
the item were surmounted. If there is any chance your polytomous
item has independent parts then consider rpf.nrm.
If your categories cannot cross then the graded response model
provides a little more information than the nominal model.
Stronger a priori assumptions offer provide more power at the cost
of flexibility.